It's in the books in the key of D, basically a guitar key, and considering the Brazilian roots of this tune, that makes sense. But a key change is in order when converting to a straight ahead jazz tune. Dexter Gordon recorded Wave in C (D for tenor sax) and Paul Desmond recorded it in F (D for alto sax). Consider it in key of C, and that also helps the comparison with the Roman numeral version.
Interestingly, it's a 12 bar A section, 8 bar bridge. The 12 measure A section is analogous to the blues form. It's a bit of a stretch, but the comparison may serve as an aid to memorizing the progression.
The first 4 could be compared to a blues with a "quick IV" except the "IV" in measure 2 is shown as a bvi diminished chord - the notes in a full diminished on b6 are b6 - 7 - 2 - 4 of the key, several ways to realize that chord. The 8 tone scale for a full diminished adds 4 tones each a whole step above the given tones. The scale for measure 2 could be Ab Bb B C# D E F G. Measure 3 is a v minor, measure 4 a I7, as it would be in a 12 bar blues.
Measure 5 is a IV chord, measure 6 a minor iv - as in a blues where measure 6 sometimes is often altered to iv, bVII or #iv dim. Instead of a return to I in measure 7 the song goes to variations on III dominant (iii a substitute for I, so III7 is not such a stretch). The A7 (VI7) in measure 8 is a bit unconventional - but the cadence that appears in measures 9 & 10 is close to the spirit of the blues. A jazz blues would offer ii - V7 in measure 9-10. Jobim gives us a II chord to V7, modified by adding preceding chords, vim7-II9 followed by bVI9-V7 alt.
Instead of a resolution to I in measures 11-12 we get a shift to parallel minor, Cm7-F7 2 times - or more. As an option, later, say after the third time through A, one could extend the im - IV pattern to several repetitions, and the next soloist would take over at letter A!
The bridge takes us to ivm7 - bVII7 - bIII in the first 4 bars. Then either a parallelism of biiim7 - bVI7 - bII - V7(alt) in 5-8 of the bridge - or bIIIsus-bVI, bIIIsus-bVI, bII, V7(alt) to turn around for last A. In key of C the bridge is simply Fm-Bb7 Eb__, Ebm7-Ab7 Db to G7+5 (or G7+9). I took some liberties and arranged 3-4 as the cliche of EbM7-Eb6 % (rpt) and instead of a long ii-V in Db measures 5-6 use Ebsus-Ab7 % (rpt)
So a full arrangement would be: Vamp in on Cm7-F7, A A B A, solos on A A B A with optional extended vamp at end of each solo, vamp out on Cm7-F7, maybe ritard to a C69 last chord.